HUNTER and ZVVEIFEL: SWIMMING SPEED AND TAIL BEAT FREQUENCY 



Table 1. — Swimming speed-tail beat frequency equations for seven species 



of fish. 



Species 



r = a, i2/3 + a^ ' F 



90% support-plan© 

 interval^ 



Triakt! hftiUi 



Trachurul symrmtricu! 



Scomber japonicul- 



Leucucuj Uuciicus 



Carasiiul auratus 



Salmo gairdneri 



V = -1.39i-^' + 0.93Z. • F 



l.SOL-^^ + 0.83i * F 



V = -2.20L~^'^ + 0.82i * F 



-2.71 <«!< -0.01 

 0.77 < Oj < 1 .09 



V = 2.49 



-3.28 <«!< -1.59 

 0.78 <a^< 0.88 



! , = 12.39 



-3.18 <a^< -1.13 

 0.76 <aa< 0.88 



s , = 12.31 



—2.21 <Qt.< -0.86 

 0.71 <a3< 0.78 



J , = 7.78 



-1.47 <aj< 0.17 

 0.61 <a^< 0,74 



-2.63 <a^< 0.13 

 0.59 < Oj < 0.69 



Sardtnopl sagax 



0.49i-^^ + 0,50i • / 



-1.61 <0!^< 2.58 

 0.39 <a3< 0.62 



^Simultaneous confidence intervals for alt parameters (Conway, Glass, and Wilcox, 1970). 



"On© deviant fish omitted; if fish included F 



-0.53L 



!/3 



+ 0.66i • F, and s. = 21.31. 



tional to L--'^ The elevation of the line relating 

 Vo to length for a species was estimated by as- 

 suming that the lowest observed speed fell on 

 that line. For Trachunis and Carassius we 

 recalculated the elevation for a slope of 2/3. 

 Our estimates of Vo and Fo were not definitive. 

 For Trachunis no fish were tested at speeds 

 close to the theoretical minimum. Our esti- 

 mates based on the theoretical minimum speed 

 were closest to the observed minimum speeds in 

 fish 9.4 cm total length and larger (Table 2) 

 because in these larger fish the test speeds were 

 sufiiciently low for fish to swim with pectoral 

 fins fully extended, an event that occurs near 

 the minimum swimming speed (Magnuson, 

 1970). For Carassius the agreement between 

 the theoretical estimate of minimum speed and 

 observed minimum speeds was better (Table 5). 

 The explanation for this is that the techniques 

 used by Bainbridge (1958) permitted estimates 

 at much lower speeds than the one we used. 

 These data clearly show that in neither Trach- 



unis (Table 2) nor Carassius (Table 5) was 

 either Vo or Fo seriously overestimated. We feel 

 that our estimates for these two species were 

 reliable. 



The fit to the general equation was good in 

 all species (Figure 5, Table 6). The intercept 

 for the regression line did not differ from zero 

 and the scatter at low velocities was less than 

 it was when no intercept correction was used 

 (see figures in Bainbridge (1958) for compar- 

 ison) . The regression coefficient, K, in our equa- 

 tion diff'ered among species. For the five species 

 for which significant data were available, it was 

 the highest in Trachunis and lowest in Salmo. 

 Since amplitude was a constant, these results 

 implied that the speed output per beat of the 

 caudal fin was greater in Trachunis and Scomber 

 than it was in Salmo and Carassius. In Scomber, 

 the coefficient, K, may be uncertain because the 

 values of one of the five fish tested deviated con- 

 siderably from the rest. In Figure 5, all of the 

 values to the right of the regression line above 



261 



